Having beaten Cartagines 3-0 last Sunday and Alajuelense 3-1 on Wednesday at the National Stadium in San Jose, the Cottagers returned to the same venue on Saturday to face Deportivo Saprissa.
With new chairman Shahid Khan watching from the stands, David Ramirez opened the scoring for the Costa Ricans on 26 minutes.
But Fulham pulled level within three minutes as captain for the night Bryan Ruiz tricked his marker after collecting Hugo Rodallega's chipped pass and slid the ball home.
On 39 minutes, Mesca delivered a superb cross from the left flank which Rodallega met with a diving header to put Fulham in front.
However, a classy individual effort from Saprissa's Diego Estrada levelled matters again on 69 minutes and with no further goals in normal time, the friendly went to a penalty shootout.
Fulham won 5-3 on spot-kicks, with Giorgos Karagounis, Ruiz, Sascha Riether, Ashkan Dejagah and Rodallega all on target.
After the game, Jol told Fulham's website: "We are still looking for one or two players to make it 100 percent. You saw 22, 23 players and they did their best.
"We would like to be in the top 10. We were a bit unlucky last year because we missed a lot of players - Mousa Dembele went, then of course top scorer Clint Dempsey went and Danny Murphy, then Mahamadou Diarra was injured.
"Steve Sidwell was suspended for seven games, so it was too much probably on the shoulders of Bryan and I feel this year will be our year again as we have good quality and I feel that we are very positive."
Fulham's pre-season preparations continue next Sunday with a friendly away to Werder Bremen.